Mark Scheme (Results) - Pearson qualifications...Aug 22, 2018 · A1 SCB2 for 24102. Question...

Mark Scheme (Results) Summer 2018 Pearson Edexcel International GCSE In Mathematics A (4MA0) Paper 3H

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Summer 2018

Publications Code 4MA0_3H_1806_MS

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General Marking Guidance All candidates must receive the same treatment. Examiners must

mark the first candidate in exactly the same way as they mark the

last.

Mark schemes should be applied positively. Candidates must be

rewarded for what they have shown they can do rather than

penalised for omissions.

Examiners should mark according to the mark scheme not

according to their perception of where the grade boundaries may

lie.

There is no ceiling on achievement. All marks on the mark scheme

should be used appropriately.

All the marks on the mark scheme are designed to be awarded.

Examiners should always award full marks if deserved, i.e. if the

answer matches the mark scheme.

Examiners should also be prepared to award zero marks if the

candidate’s response is not worthy of credit according to the mark

scheme.

Where some judgement is required, mark schemes will provide the

principles by which marks will be awarded and exemplification may

be limited.

When examiners are in doubt regarding the application of the mark

scheme to a candidate’s response, the team leader must be

consulted.

Crossed out work should be marked UNLESS the candidate has

replaced it with an alternative response.

Types of mark

o M marks: method marks

o A marks: accuracy marks

o B marks: unconditional accuracy marks (independent of M

marks)

Abbreviations

o cao – correct answer only

o ft – follow through

o isw – ignore subsequent working

o SC - special case

o oe – or equivalent (and appropriate)

o dep – dependent

o indep – independent

o eeoo – each error or omission

No working

If no working is shown then correct answers normally score full marks

If no working is shown then incorrect (even though nearly correct)

answers score no marks.

With working

If there is a wrong answer indicated on the answer line always check

the working in the body of the script (and on any diagrams), and

award any marks appropriate from the mark scheme.

If it is clear from the working that the “correct” answer has been

obtained from incorrect working, award 0 marks.

Any case of suspected misread loses A (and B) marks on that part,

but can gain the M marks.

If working is crossed out and still legible, then it should be given any

appropriate marks, as long as it has not been replaced by alternative

work.

If there is a choice of methods shown, then no marks should be

awarded, unless the answer on the answer line makes clear the

method that has been used.

If there is no answer on the answer line then check the working for

an obvious answer.

Ignoring subsequent work

It is appropriate to ignore subsequent work when the additional work

does not change the answer in a way that is inappropriate for the

question: eg. Incorrect cancelling of a fraction that would otherwise

be correct.

It is not appropriate to ignore subsequent work when the additional

work essentially makes the answer incorrect eg algebra.

Transcription errors occur when candidates present a correct answer

in working, and write it incorrectly on the answer line; mark the

correct answer.

Parts of questions

Unless allowed by the mark scheme, the marks allocated to one part

of the question CANNOT be awarded in another.

International GCSE Maths 3H

Apart from Questions 6b, 11, 13, 14, 17, 21c (where the mark scheme states otherwise), the correct answer, unless clearly obtained by

an incorrect method, should be taken to imply a correct method.

Question Working Answer Mark Notes

1 (a) 3167.352831

13.7

231.19(3637) 2 M1 For 3167.35(2831) rounded or truncated to

at least 2 decimal places or for 13.7 or for

231.(193....) rounded or truncated to at least

3 significant figures A1 Accept rounded or truncated to at least 2

decimal places

(b) 230 1 B1 ft from (a) provided more than 3 significant

figures

2 62.8 ÷ 8 (=7.85) or 12 ÷ 8 (=1.5) or

62.8 ÷ 2 (=31.4) or 62.8 ÷ 4 (15.7) or

8 62.8 12x or 8 753.6x

94.20 2 M1 Or for a complete method

Eg 12

62.88

or 62.8 1.5

A1

Accept 94.2


3 (a) 2.25 or 2 × 60 + 15 (=135) 18 3 M1

For 2.25 or 2 × 60 + 15 or 135

Eg 40 ÷ 2.25 or

140 2

4 or

40

2.25or

40

12

4

or 40 ÷ ‘135’ × 60 or 160

9

oe

M1 For a complete method

A1

Accept 7

179

or 17.7(777...)

rounded or truncated to at least 3

significant figures

SCB1 for 40 ÷ 2.15 or 18.6(046)

rounded or truncated to at least 3

significant figures

(b) 28 500 × 0.024 oe (=684) 29 184 3 M1

M2 for 28 500 × 1.024

oe 28 500 + “684” M1 dep A1

(c) 702 ÷ 3 (=234) or 100 ÷ 3 (=33.3…) or

1.03x = 702 + x or 0.03 702x oe

23 400 3 M1 M2 for 702 ÷ 0.03 oe

“234” × 100 or “33.3…” × 702 M1 dep A1 SCB2 for 24102


4 (a) Reflection in the line with equation x

= 6 2 B1

B1

for reflection

for x = 6

NB. Award no marks if more than

one transformation given

(b) trapezium with vertices

(4, −2) (4, −4) (7, −6)

(7, −2)

2 B2 If not B2 then award B1 for

trapezium in correct orientation or

a trapezium with 3 vertices correct

5 (a) x + 2x + 3x + x + x or 8x 1

8 oe

3 M1

x + 2x + 3x + x + x = 1 or 8x = 1 or

8

x

x

M1

A1

Oe

(b) 3 ×

1" " 200

8 or

3200

8

x

x or

200 3x or 600x

75 2 M1

ft from (a) if 0 < "(a)" < 1

A1 ft from (a) if 0 < "(a)" < 1

SCB1 for an answer of 25

Only award A1 for numerical

answers


6 (a) m(m + 7) 1 B1

(b) 7x + 21

eg 7x – 5x = −4 − 21 or 2 25x or

21 4 5 7x x or 25 2x

−12.5 oe 3 M1 for 7x + 21 or division of all terms by 7

M1 for isolation of terms in x on one side of a

correct equation

ft from 7x + 3 = 5x – 4

(eg 7x – 5x = −4 − 3 or 2 7x )

A1 dep on at least M1 awarded

(c) y2 + 9y – 4y − 36 y2 + 5y − 36 2 M1 for 3 terms correct or all 4 terms correct

ignoring signs or

y2 + 5y + …. or

…… + 5y − 36 A1

(d) 9 664e f 2 B2 For 9 6

64e f

Accept 9 6

64 e f

If not B2 then

B1 for 3 3 3 2 34 e f

or

ae9f 6 a ≠ 64 or

64emf 6 m ≠ 9 or

64e9f n n ≠ 6


7 Eg (HJ²=) 16.22 – 11.82 (= 123.2) or

(HJ²=) 262.44 – 139.24

Eg (HJ=)2 2

16.2 11.8 or "123.2"

11.1 3 M1

M1

A1

For squaring and subtracting

Dep (for square rooting)

For 11.09 – 11.1

Award M2 for trigonometry used only

for a complete method

8 (a)

(b)

− 3 – 4 < x < 9 – 4 or −7 < x or x < 5 −7 < x < 5

2

2

M1

A1

B2

Or for 7 and 5

Accept 7x and 5x

B1 for a line that extends from 2 to 5

or

for both correct circles in correct place

with either no line or incorrect lines

or

for a correct circle at 5 with line to the

left (with or without arrow)

or

for a correct circle at −2 with line to

the right (with or without arrow)

1 2 3 4 5 6 -1 -2 -3 0 y


9 (a) 8.2 × 107 1 B1 Cao

Accept 78.20 10

(b)

(c)

(1.898 × 1027) ÷ (3.285 × 1023)

0.000 029

5800

1

2

B1

M1

A1

Cao

Condone omission of brackets

Accept 5700 - 5800

Accept answers in standard form


10 (a) 164 < w ≤ 168 1 B1

(b) 162 × 12 + 166 × 20 + 170 × 14 + 174 × 7 + 178 × 4 + 182 ×

3

or

1944 + 3320 + 2380 + 1218 + 712 + 546

10120 3 M2

A1

freq × all correct midpoint values stated

(or evaluated) with intention to add

(condone any two errors in midpoints or

frequencies)

If not M2 then award M1 for all products

w × f (and w is consistently within the

interval, including end values) and

intention to add (condone any two errors

in their midpoints or frequencies)

SCB2 for 168.(666...) rounded or

truncated to at least 3 significant figures


10 (c) 12, 32, 46, 53, 57, 60 1 B1

(d) (164,12), (168,32), (172, 46), (176,53), (180,57), (184,60)

Correct cf graph 2 M1

A1

For at least 4 points plotted correctly at

end of interval or

for all 6 points plotted consistently within

each interval in the freqency table at the

correct height. (Eg, using values of 162,

166, 170, etc, on x axis)

Accept curve or line segments

Accept curve that is not joined to (160,0)

(e) Eg 171.5 (Q3) 164.5 (Q1)

6-8 2 M1 For a correct method to find lower and

upper quartile and an intention to

subtract

Eg for a correct reading from

45/45.75 or 15/15.25 from vertical

axis to find Q1 and Q3 and an

intention to subtract.

Ft from a cf graph

A1 Accept 6 - 8

ft from a cf graph


11 Eg +21 6 123

8 6 22

x y

x y

28 8 164

28 21 77

x y

x y

x = 5

y = −3 4 M1 For coefficient of x or y the same and correct

operation to eliminate selected variable (condone

any one arithmetic error in multiplication) or

for correct rearrangement of one equation followed

by correct substitution in the other. x = 5 or y = −3 A1 cao ( dep on M1) Eg 4 × ‘5’ + 3y = 11

x = 5 and y = −3

M1 (dep on 1st M1) for substituting their found value

into one of the equations

or

correct method of elimination to find the second

variable (as for first M1) A1 cao. Award 4 marks for correct values if at least

first M1 scored without any incorrect working.

12 Eg (y = )

(5 2) 180

5

or

360180

5 or 108

(6 2) 180

6

or

360180

6 or 120

126 4 M1

M1

M1

A1

For correct method to find y or

the size of an angle of a regular hexagon

the sum of interior angles of a pentagon or

the sum of interior angles of a hexagon or

For correct method to find y and the sum of interior

angles of a hexagon

Dep on previous two method marks.

For a correct equation in x only or

for a complete method to find x

(5 2) 180 or 540 or (6 2) 180 or 720

or 2 4 720y x or

Eg (5 2) 180

5

(= 108) and (6 2) 180 (=720)

Eg (6 2) 180 "108" 2 4x or

720 216 4x or 4 504x or

(“720” – 2 × 108) ÷ 4 or 504

4


13 6 52

8

or

26 6 16

2 4

or

26 6 16

8

or

6 2 13

8

NB: denominator must be 2 × 4 or 8 and there

must be evidence for correct order of

operations in the numerator

Accept 36 in place of 2

6

0.151, −1.65 3 M2 Or for

26 6 4 4 1

2 4

and

3 13

4

(allow partial correct evaluation)

If not M2 then

M1 for 2

6 6 4 4 1

2 4

Condone one sign error in substitution

Allow partial evaluation

A1 For 0.151 to 0.1514 and −1.65 to −1.6514

dep on at least M1 without any incorrect working.

SCB2 for 0.151 to 0.1514 or −1.65 to −1.6514 if

method for M1 shown without any incorrect

working.


14 (Angle GDE =) 98÷2 (=49) or

(reflex angle GOE =) 360 – 98 (=262)

131 4 M1

(Angle GFE =) 180 – “49” or “262”÷2 or 131

Angle at the centre is twice the angle at the

circumference AND

The opposite angles in a cyclic quadrilateral

total 180° or

Angle at centre is twice angle at circumference

AND Angles at a point sum to 360o

M1 dep

A2 for 131º and fully correct reasons

If not A2 then A1 for 131o and one correct circle

theorem reason

Eg Accept double in place of twice, origin (O) in

place of centre and edge/arc in place of

circumference

Accept ‘angle at circumference is half the angle at

the centre’ oe

Accept 'angle at the centre is twice angle inscribed

on the circle

Accept supplementary in place of 'total 180º'

SCB2 for one correct circle theorem if method for

first M1 seen


15 (a) Eg

2( 3)

( 3) ( 3)

x x

x x x x

or

2( 3)

( 3)

x x

x x

6

( 3)

x

x x

3 M1 For a correct expression with a correct common

denominator

Condone brackets in denominator expanded

Eg 2 6

( 3) ( 3)

x x

x x x x

or

2 6

( 3)

x x

x x

M1

For a correct expression with brackets expanded

Condone brackets in denominator expanded

A1 Accept

2

6

3

x

x x

SCB1 for 2 3

( 3) ( 3)

x x

x x x x

or

2 3

( 3)

x x

x x

Do not ISW (b) (3x + 2)(3x – 2) 3 2

5

x

x

3 M1 (3x – 2)(x – 5) M1 indept A1 Do not ISW


16 Eg

sin sin 78

12.7 18.5

R or

12.7 18.5

sin sin 78R or

12.7 sin 78(sin )

18.5R oe

Eg1 sin 78

( ) sin 12.718.5

R

or

1( ) sin 0.671(485...)R

or 42.1(817...)

Eg

112.7 18.5 sin(180 78 "42.1(817...)")

2

112.7 18.5 sin(59.8(182...)

2 )

102 4 M1

M1

M1

A1

For correct use of the sine rule

For the correct method to find R

Accept (R =) 42.1(817...) rounded or truncated to at

least 3 significant figures or

(R=) 42

Dep on M2

For the correct method to find the area of triangle PQR

For 101 – 102


17 Eg

6 10 2

2 2

or

(6 10) 2

4

or

6 2 20

4

or

6 5 2 2

2 2

or

6 2 10 2

4

3 2 5 3 M1

For the correct method to rationalise

the denominator or

for 6

52

Eg

6 2 2 5

4

or

6 2 2 5

4 4 or

6 25

4

Accept 2 in place of 4 for both method marks

M1 For partial simplification (the

denominator must be rationalised at

this stage).

Implies first M1

A1 Correct solution only

dep on M2

18 (a) ( s =) 3 + t −1

2

1

t

2 M1 For 11

tt

A1 oe

Eg 2t

(b) −1 × −2t −3 or −1 × −2(6) −3 oe 1

108

2 M1 ft from (a) provided of form

a + tn, where a is a constant and

n < 0 A1 Oe

Eg 0.00925(925...) rounded or

truncated to at least 3 significant

figures Accept answers in standard form


19 Eg 21

15 183

or 1350π or 424(1.150...)

or

2 2115 18 15 20

3 or

1350 π + 4500 π or 5850 π or

424(1.150...) + 141(37.1...) or 183(78.3...)

24.7 5 M1 For correct method to find the volume of the cone

or volume of the container

Accept 424(1.150...), 141(37.1...) and 183(78.3...)

rounded or truncated to at least 3 significant figures

9 × 1000 − “1350 π” or 475(8.84…) or

"5850 π" − 9 × 1000 or 937(8.31...)

“475(8.84…)” = × 152 × h or

"937(8.31...)" = × 152 × h

2

"475(8.84...)"

15 or 6.73(239…) or

2

"937(8.31...)"

15 or 13.2(676...)

M1

Accept 475(8.84…) and 937(8.31...) ... rounded or


M1

M1

A1

Accept 6.73(239…) and 13.2(676...) rounded or


Accept 24.7 – 24.8

Allow use of litres or cm³ for method marks (but not

mixed in the same calculation)


20 3 2 6

9 8 7 or

1

14 oe or 0.071(428...) or

6 5 4

9 8 7 or

5

21oe or 0.238(095...)

228

504

4 M1

Accept 0.071(428...), 0.238(095...)

and 0.214(285...) rounded or truncated

to at least 3 decimal places

Eg

3 2 6

9 8 7 AND

6 5 4

9 8 7 or

3 2 6 3 6 2 6 3 2

9 8 7 9 8 7 9 8 7 oe or

3 2 63

9 8 7 or

3

14oe or 0.214(285...)

M1

Eg

3 2 6 6 5 43

9 8 7 9 8 7 oe or

3 2 1 6 5 31 ( 3 )

9 8 7 9 8 7 or

231

42 oe

M1

A1

For a complete method

oe

Eg 19

42

Accept 0.45(238...) rounded or

truncated to at least 2 decimal

places

With Replacement (maximum 2 marks)

3 3 6

9 9 9 or

2

27oe or 0.074(074...) or

6 6 6

9 9 9 or

8

27 oe or 0.296(296...)

3 3 6 6 6 63

9 9 9 9 9 9 or

14

27 or 0.51(851...) oe

3 3 3 6 6 31 ( 3 )

9 9 9 9 9 9 or

131

27 oe

M1

M1

Accept 0.074(074...), 0.296(296...)

and 0.222(222...) rounded or truncated

to at least 3 decimal places

For a complete method

Accept 0.51(851...) rounded or

truncated to at least 2 decimal

places

SC B2 for an answer of 378

729 oe


21 (a)

(b)

Eg y – 3 = −2x or 2x = 3 – y or 3

2 2

yx

3 2x y or 2 3y x or 3

2 2

xy

11

3

2

x

0.5, 3.5

1

2

5

B1

M1

A1

For correct first step

or 3

2

yor

3

2

y

oe

Eg 3

2 2

x or

3

2

x

(c) Eg (gf(x) =) (3 – 2x)2 – 5 or (ff(x) =) (3 – 2(3 – 2x))

Eg (3 – 2x)2 – 5 = 3 – 2(3 – 2x) or

(gf(x) =) 9 – 6x – 6x + 4x2 – 5 or2

4 12 4x x or

(ff(x) =) 3 6 4x or 4 3x oe

Eg 9 – 6x – 6x + 4x2 – 5 = 3 – 6 + 4x or 2

4 12 4 4 3x x x

Eg 4x2 – 16x + 7 (= 0) or (2 1)(2 7)x x (=0) oe

M1

M1

M1

M1

A1

For gf(x) or ff(x)

For a correct equation or

gf(x) brackets expanded

correctly or

ff(x) brackets expanded correctly

For a correct equation with all

brackets expanded correctly

For a correct 3-term quadratic

(all terms on the same side)

oe

Dep on at least M3

Mark Scheme (Results) - Pearson qualifications...Aug 22, 2018 · A1 SCB2 for 24102. Question...

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